On the observability inequality of coupled wave equations: the case without boundary. (English) Zbl 1441.35156
The authors study the observability and controllability of wave equations coupled by first or zero order terms on a compact manifold. By duality, they obtain the controllability of the dual control system in a finite co-dimensional space. Finally, they provide some concrete examples as applications where the unique continuation property indeed holds.
Reviewer: Kaïs Ammari (Monastir)
MSC:
| 35L52 | Initial value problems for second-order hyperbolic systems |
| 35B60 | Continuation and prolongation of solutions to PDEs |
| 93B05 | Controllability |
| 93B07 | Observability |
| 58J45 | Hyperbolic equations on manifolds |
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